A 5 m long wire of resistance 1 omega carries a current of 5 A. (a) What is the

Question

A 5 m long wire of resistance 1 omega carries a current of 5 A. (a) What is the potential difference across the wire? (b) What is the magnitude of the electric field in the wire? (a) How long is a 14 gauge copper wire that has a resistance of 12.0 omega? (b) How much current will it carry if a 123-V potential difference is applied across its length? A battery has an emf of 12.0 V. How much work does it do in 1 s if it delivers a current of 2.6 A? A 12.0 V automobile battery that has a negligible internal resistance can deliver a total charge of 149 Ah. (a) What is the amount of energy stored in the battery? (b) After studying all night for a calculus test, you try to drive to class to take the test. However, you find that the car?s battery is dead because you had left the headlights on! Assuming the battery was able to produce current at a constant rate until it died, how long were your lights on? Assume the pair of headlights together operates at a power of 100 W.

Explanation / Answer

1)

a)

Potential difference

V=IR =1*5=5 Volts

b)

Electric field

E=V/d =5/5 =1 V/m

2)

a)

Diameter of 14 gauge copper wire

d=1.628 mm

Area

A=pi*d2/4 =pi*(1.628*10-3)2/4 =2.08*10-6 m2

Resistance

R=pL/A

12=(1.7*10-8)*L/(2.08*10-6)

L=1469.4 m

b)

Current

I=V/R=123/12

I=10.25 A

3)

Work done

W=V*I*t =12*1*2.6

W=31.2 J

4)

a)

Energy

E=(149*60*60)*12

E=6.44 MJ

b)

t=E/P =6.44*106/100

t=17.88 hours

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